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Hakan E. Türeci

Publications and source records attributed to Hakan E. Türeci.

At least 19 recordsLinked to original sources
arXiv2026

Unifying Physical Backpropagation

Physical computing systems exploit device dynamics for computation, but their gradient-based optimization is challenging: backpropagation through a digital twin suffers from a model-reality gap. On-device gradient computation could resolve this issue, and a handful of theoretical and experimental studies have proposed ways to achieve it. Yet a unifying theory identifying when a physical system can compute the gradient of its own performance has been missing. Here we develop such a unification based on the adjoint method: we identify sufficient conditions under which the adjoint field required for formally exact gradients can be generated on the same hardware that performs the computation. Linear and nonlinear systems obey fundamentally different conditions: for linear systems, damping or gain is admissible provided reciprocity is preserved. For nonlinear trajectory systems, the sufficient conditions are reciprocity of the linearized system and the existence of a time-reversal mirror. Algorithmically, the nonlinear case requires infinitesimal nudging, whereas linear systems admit a finite-amplitude experiment. We recover (quantum) Equilibrium Propagation, Hamiltonian echo backpropagation, fully forward mode training and in situ gradient methods in integrated-photonic and free-space-optical systems. Finally, we show that reciprocity is a special case of more general intertwining conditions. For linear systems, these permit exact on-device gradients in a class of non-Hermitian, non-reciprocal systems. For nonlinear trajectories, they combine with generalized time-reversal mirrors to cover, e.g., PT-symmetric equations. The framework also includes time-dependent parameters and Onsager-reciprocal dynamics, providing a unified basis for formally exact physical learning.

cond-mat.dis-nn↗
arXiv2026

End-to-end Optimization of Single-Shot Quantum Machine Learning for Bayesian Inference

We introduce an end-to-end optimization strategy for quantum machine learning that directly targets performance under finite measurement resources, where learning objectives are defined directly at the level of task performance. The method is applied on a Bayesian quantum metrology task since it provides a natural testbed with known fundamental limits and scaling with system size. The sampling-aware hybrid algorithm achieves a single-shot risk within 1 dB of the -20 dB Bayesian limit using 32 qubits. We extend the Bayesian framework from parameter estimation to global function inference, where the task is to infer a target function of the sensor input drawn from an arbitrary prior, and we demonstrate a clear computational-sensing advantage for direct functional inference over indirect reconstruction. We relate the corresponding Bayesian risk to the Capacity metric and argue that the Resolvable Expressive Capacity provides a natural measure of the space of functions accessible in a single shot. The resulting eigentask analysis identifies noise-robust feature combinations that yield compact estimators with improved accuracy and reduced optimization cost in resource-limited or real-time on-device settings. Going beyond the irreducible statistical uncertainty associated with finite measurement records, we study implementation-induced distortions of the sensor response focusing on representative imperfections arising from readout errors and static coherent gate disorder. We show that when these imperfections are stationary across training and inference, end-to-end optimization can adapt the quantum circuit and classical estimator to the implemented hardware response, preserving high inference performance over a broad range of imperfection strengths.

quant-ph↗
arXiv2026

Single-shot Quantum State Classification via Nonlinear Quantum Amplification

Quantum amplifiers are intrinsically nonlinear systems whose performance limits are set by quantum mechanics. In quantum measurement, amplifier operation is conventionally optimized in the linear regime by maximizing signal-to-noise ratio, an objective that is well-suited to parameter estimation but is typically insufficient for more general tasks such as arbitrary quantum state discrimination. Here we show that single-shot quantum state classification can benefit from operating a quantum amplifier outside the linear regime, when the measurement chain is optimized end-to-end for a task-specific cost function. We analyze a realistic superconducting readout architecture that includes state preparation, cryogenic nonlinear amplification, and room-temperature detection with finite noise. By introducing performance metrics tailored to state discrimination, we identify operating regimes in which nonlinear amplification provides a measurable advantage and clarify the trade-offs that ultimately limit classification fidelity. Building on these results, we propose a qubit readout architecture without cavity displacement that exploits nonlinear amplification to enhance single-shot state discrimination performance. Our results establish the practical value of nonlinear quantum amplifiers for quantum state discrimination and lay the foundation for a broader program to develop a general, end-to-end framework for resource-constrained optimization of nonlinear amplification in quantum information processing tasks.

quant-ph↗
arXiv2026

Measurement-Adapted Eigentask Representations for Photon-Limited Optical Readout

Optical readout in low-light imaging is fundamentally limited by measurement noise, including photon shot noise, detector noise, and quantization error. In this regime, downstream inference depends not only on the optical front end, but also on how noisy high-dimensional sensor measurements are represented before classification or decision-making. Here we show that eigentasks provide a measurement-adapted representation for optical sensor outputs by ordering readout features according to their resolvability under noise. Using experimental data from a lens-based optical imaging system and a reanalysis of published data from a single-photon-detection neural network, we find that eigentask representations frequently outperform standard baselines including principal component analysis and filtering-based compression. The advantage is most pronounced in photon-limited, few-shot, and higher-difficulty classification regimes. In few-shot MPEG-7 classification, for example, the advantage over other methods reaches about 10 percentage points as the number of classes increases. In these settings, eigentasks yield more informative low-dimensional features and improve sample-efficient downstream learning. These results identify measurement-adapted representation as a promising strategy for optical inference when photon budget, acquisition time, and task complexity are constrained.

physics.optics↗
arXiv2026

Model Order Reduction for Open Quantum Systems Based on Measurement-adapted Time-coarse Graining

Model order reduction encompasses mathematical techniques aimed at reducing the complexity of mathematical models in simulations while retaining the essential characteristics and behaviors of the original model. This is particularly useful in the context of large-scale dynamical systems, which can be computationally expensive to analyze and simulate. Here, we present a model order reduction technique to reduce the time complexity of open quantum systems, grounded in the principle of measurement-adapted coarse-graining. This method, governed by a coarse-graining time scale $τ$ and the spectral band center $ω_0$, organizes corrections to the lowest-order model which aligns with the RWA Hamiltonian in certain limits, and rigorously justifies the resulting effective quantum master equation (EQME). The focus on calculating to a high degree of accuracy only what can be resolved by the measurement introduces a principled regularization procedure to address singularities and generates low-stiffness models suitable for efficient long-time integration. Furthermore, the availability of the analytical form of the EQME parameters significantly boosts the interpretive capabilities of the method. As a demonstration, we derive the fourth-order EQME for a challenging problem related to the dynamics of a superconducting qubit under high-power dispersive readout in the presence of a continuum of dissipative waveguide modes. This derivation shows that the lowest-order terms align with previous results, while higher-order corrections suggest new phenomena.

quant-ph↗
arXiv2026

Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics

Quantum information is typically fragile under measurements and environmental coupling. Remarkably, we find that its lifetime can scale exponentially with system size when the environment is continuously monitored via mid-circuit measurements -- regardless of bath size. Starting from a maximally entangled state with a reference, we analytically prove this exponential scaling for typical Haar random unitaries and confirm it through numerical simulations in both random unitary circuits and chaotic Hamiltonian systems. In the absence of bath monitoring, the lifetime exhibits a markedly different scaling: it grows at most linearly -- or remains constant -- with system size and decays inversely with the bath size. We further extend our findings numerically to a broad class of initial states. In the intermediate regime of partial monitoring, we identify and prove a two-scale transition, where the QMI decays logarithmically at microscopic time scales but linearly at macroscopic time scales.} We discuss implications for {monitored quantum circuits in the weak measurement limit, quantum algorithms such as quantum diffusion models and quantum reservoir computing, and quantum communication. Finally, we experimentally verify the gap of persisted information on IBM Quantum hardwares.

quant-ph↗
arXiv2026

Overcoming the Coherence Time Barrier in Quantum Machine Learning on Temporal Data

Practical implementation of many quantum algorithms known today is limited by the coherence time of the executing quantum hardware and quantum sampling noise. Here we present a machine learning algorithm, NISQRC, for qubit-based quantum systems that enables inference on temporal data over durations unconstrained by decoherence. NISQRC leverages mid-circuit measurements and deterministic reset operations to reduce circuit executions, while still maintaining an appropriate length persistent temporal memory in quantum system, confirmed through the proposed Volterra Series analysis. This enables NISQRC to overcome not only limitations imposed by finite coherence, but also information scrambling in monitored circuits and sampling noise, problems that persist even in hypothetical fault-tolerant quantum computers that have yet to be realized. To validate our approach, we consider the channel equalization task to recover test signal symbols that are subject to a distorting channel. Through simulations and experiments on a 7-qubit quantum processor we demonstrate that NISQRC can recover arbitrarily long test signals, not limited by coherence time.

quant-ph↗
arXiv2026

High-fidelity Quantum Readout Processing via an Embedded SNAIL Amplifier

Scalable, high-fidelity quantum-state readout remains a central challenge in the development of large-scale superconducting quantum processors. Conventional dispersive readout architectures depend on bulky isolators and external amplifiers, introducing significant hardware overhead and limiting opportunities for on-chip information processing. In this work, we propose a novel approach that embeds a nonlinear Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) into the readout chain, enabling coherent and directional processing of readout signals directly on-chip. This embedded SNAIL platform allows frequency-multiplexed resonators to interact through engineered couplings, forming a tunable readout-amplifier-output architecture that can manipulate quantum readout data \textit{in situ}. Through theoretical modeling and numerical optimization, we show that this platform enhances fidelity, suppresses measurement-induced decoherence, and simplifies hardware complexity. These results establish the hybridized SNAIL as a promising building block for scalable and coherent quantum-state readout in next-generation processors.

quant-ph↗
arXiv2025

Long-time soliton dynamics via a coarse-grained space-time method

We investigate the long-time dynamics of the Sine-Gordon (SG) model under a class of perturbations whose quantum field theoretic analog - via bosonization - corresponds to the massive Schwinger model describing 1+1D relativistic QED of Dirac fermions. Classical SG solutions offer critical insight into non-perturbative effects in this quantum theory, but capturing their long-time behavior poses significant numerical challenges. To address this, we extend a coarse-graining method to spacetime using a dual-mesh construction based on the Minkowski-metric. We first validate the approach against the well-studied variant of the SG model describing magnetic fluxon dynamics in Josephson transmission lines (JTLs), where analytical and numerical benchmarks exist. We then apply the method to the Schwinger-inspired SG model and uncover long-lived bound states - "Schwinger atoms" - in which a soliton is trapped by a fixed central charge. In certain regimes, the system exhibits limit cycles that give rise to positronium-like states of oppositely charged solitons, while in others such formation is suppressed. Accessing such long-time solutions requires a rigorous implementation of outgoing boundary conditions on a finite computational domain that provide radiative dissipation to allow relaxation toward states that exist only in an infinite domain. Here we provide such a construction. Our results also suggest the possibility of analog quantum simulation of relativistic quantum field theories with JTLs. These results demonstrate the utility of spatio-temporal coarse-graining methodology for probing non-perturbative structure formation in non-linear field theories.

quant-ph↗
arXiv2025

Quantum theory of the Josephson junction between finite islands

Superconducting circuits comprising Josephson junctions have spurred significant research activity due to their promise to realize scalable quantum computers. Effective Hamiltonians for these systems have traditionally been derived assuming the junction connects superconducting islands of infinite size. We derive a quantized Hamiltonian for a Josephson junction between finite-sized islands and predict measurable corrections to the qubit frequency and charge susceptibility to test the theory.

quant-ph↗
arXiv2025

A neural processing approach to quantum state discrimination

Although linear quantum amplification has proven essential to the processing of weak quantum signals, extracting higher-order quantum features such as correlations in principle demands nonlinear operations. However, nonlinear processing of quantum signals is often associated with non-idealities and excess noise, and absent a general framework to harness nonlinearity, such regimes are typically avoided. Here we present a framework to uncover general quantum signal processing principles of a broad class of bosonic quantum nonlinear processors (QNPs), inspired by a remarkably analogous paradigm in nature: the processing of environmental stimuli by nonlinear, noisy neural ensembles, to enable perception. Using a quantum-coherent description of a QNP monitoring a quantum signal source, we show that quantum nonlinearity can be harnessed to calculate higher-order features of an incident quantum signal, concentrating them into linearly-measurable observables, a transduction not possible using linear amplifiers. Secondly, QNPs provide coherent nonlinear control over quantum fluctuations including their own added noise, enabling noise suppression in an observable without suppressing transduced information, a paradigm that bears striking similarities to optimal neural codings that allow perception even under highly stochastic neural dynamics. Unlike the neural case, we show that QNP-engineered noise distributions can exhibit non-classical correlations, providing a new means to harness resources such as entanglement. Finally, we show that even simple QNPs in realistic measurement chains can provide enhancements of signal-to-noise ratio for practical tasks such as quantum state discrimination. Our work provides pathways to utilize nonlinear quantum systems as general computation devices, and enables a new paradigm for nonlinear quantum information processing.

quant-ph↗
arXiv2025

Mesoscopic theory of the Josephson junction

We derive a mesoscopic theory of the Josephson junction from non-relativistic scalar electrodynamics. Our theory reproduces the Josephson relations with the canonical current phase relation acquiring a weak second harmonic term, and it improves the standard lumped-element descriptions employed in circuit quantum electrodynamics by providing spatial resolution of the superconducting order parameter and electromagnetic field. By providing an ab initio derivation of the charge qubit Hamiltonian that relates traditionally free qubit parameters to geometric and material properties, we progress toward the quantum engineering of superconducting circuits at the subnanometer scale.

quant-ph↗
arXiv2024

Systematic time-coarse graining for driven quantum systems

Many recent advancements in quantum computing leverage strong drives on nonlinear systems for state preparation, signal amplification, or gate operation. However, the interplay within such strongly driven system introduces multi-scale dynamics that affects the long-time behavior of the system in non-trivial ways that are very difficult to model. Therefore, the analysis of these systems often relies on effective Hamiltonian models that introduce additional nonlinear processes which approximate the long-time dynamics so that highly oscillatory terms may be ignored. However, the removal of such high frequency transitions can only be performed rigorously within a systematic framework of time-coarse graining, which is a fundamentally irreversible operation. This implies that standard approaches with unitary effective models cannot accurately capture the long-time behavior of strongly driven nonlinear quantum systems in general. We introduce a systematic perturbation theory for obtaining the complete non-unitary effective model of the time-coarse grained (TCG) dynamics of a driven quantum system to any order in the coupling strengths. We derive a closed-form analytical formula for both unitary and non-unitary contributions, in the form of an effective Hamiltonian and non-unitary (pseudo-)dissipators. Remarkably, even though the effective theory presumes unitary time evolution at the microscopic level, the time-coarse grained dynamics is found to follow a non-unitary time evolution in general. This occurs even when there is no open heat reservoir for the system to become entangled with or dissipate into. We demonstrate the effectiveness of the new method using several typical models of driven nonlinear systems in superconducting circuits, and show that it generalizes and improves on existing methods by providing more accurate results and explaining phenomena that have not been accounted for.

quant-ph↗
arXiv2024

Practical Trainable Temporal Postprocessor for Multistate Quantum Measurement

We develop and demonstrate a trainable temporal post-processor (TPP) harnessing a simple but versatile machine learning algorithm to provide optimal processing of quantum measurement data subject to arbitrary noise processes, for the readout of an arbitrary number of quantum states. We demonstrate the TPP on the essential task of qubit state readout, which has historically relied on temporal processing via matched filters in spite of their applicability only for specific noise conditions. Our results show that the TPP can reliably outperform standard filtering approaches under complex readout conditions, such as high power readout. Using simulations of quantum measurement noise sources, we show that this advantage relies on the TPP's ability to learn optimal linear filters that account for general quantum noise correlations in data, such as those due to quantum jumps, or correlated noise added by a phase-preserving quantum amplifier. Furthermore, we derive an exact analytic form for the optimal TPP weights: this positions the TPP as a linearly-scaling generalization of matched filtering, valid for an arbitrary number of states under the most general readout noise conditions, all while preserving a training complexity that is essentially negligible in comparison to that of training neural networks for processing temporal quantum measurement data. The TPP can be autonomously and reliably trained on measurement data and requires only linear operations, making it ideal for FPGA implementations in cQED for real-time processing of measurement data from general quantum systems.

quant-ph↗
arXiv2024

Negative electrohydrostatic pressure between superconducting bodies

By applying a hydrodynamic representation of non-relativistic scalar electrodynamics to the superconducting order parameter, we predict a negative (attractive) pressure between planar superconducting bodies. For conventional superconductors with London penetration depth $λ_\text{L} \approx 100 \text{ nm}$, the pressure reaches tens of $\text{N/mm}^2$ at angstrom separations. The resulting surface energies are in better agreement with experimental values than those predicted by the Hartree-Fock theory, and the emergent electric-field screening length is comparable to that of the Thomas-Fermi theory. The model circumvents the bulk limitations of the Bardeen-Cooper-Schrieffer and Ginzburg-Landau theories to the analysis of superconducting quantum devices.

cond-mat.supr-con↗
arXiv2024

Spectral Theory for Non-linear Superconducting Microwave Systems: Extracting Relaxation Rates and Mode Hybridization

The accurate modeling of mode hybridization and calculation of radiative relaxation rates have been crucial to the design and optimization of superconducting quantum devices. In this work, we introduce a spectral theory for the electrohydrodynamics of superconductors that enables the extraction of the relaxation rates of excitations in a general three-dimensional distribution of superconducting bodies. Our approach addresses the long-standing problem of formulating a modal description of open systems that is both efficient and allows for second quantization of the radiative hybridized fields. This is achieved through the implementation of finite but transparent boundaries through which radiation can propagate into and out of the computational domain. The resulting spectral problem is defined within a coarse-grained formulation of the electrohydrodynamical equations that is suitable for the analysis of the non-equilibrium dynamics of multiscale superconducting quantum systems.

quant-ph↗
arXiv2023

Tackling Sampling Noise in Physical Systems for Machine Learning Applications: Fundamental Limits and Eigentasks

The expressive capacity of physical systems employed for learning is limited by the unavoidable presence of noise in their extracted outputs. Though present in physical systems across both the classical and quantum regimes, the precise impact of noise on learning remains poorly understood. Focusing on supervised learning, we present a mathematical framework for evaluating the resolvable expressive capacity (REC) of general physical systems under finite sampling noise, and provide a methodology for extracting its extrema, the eigentasks. Eigentasks are a native set of functions that a given physical system can approximate with minimal error. We show that the REC of a quantum system is limited by the fundamental theory of quantum measurement, and obtain a tight upper bound for the REC of any finitely-sampled physical system. We then provide empirical evidence that extracting low-noise eigentasks can lead to improved performance for machine learning tasks such as classification, displaying robustness to overfitting. We present analyses suggesting that correlations in the measured quantum system enhance learning capacity by reducing noise in eigentasks. The applicability of these results in practice is demonstrated with experiments on superconducting quantum processors. Our findings have broad implications for quantum machine learning and sensing applications.

quant-ph↗
arXiv2023

Efficient computation of coherent multimode instabilities in lasers using a spectral approach

Coherent multimode instabilities are responsible for several phenomena of recent interest in semiconductor lasers, such as the generation of frequency combs and ultrashort pulses. These techonologies have proven disruptive in optical telecommunications and spectroscopy applications. While the standard Maxwell-Bloch equations encompass such complex lasing phenomena, their integration is computationally expensive and offers limited analytical insight. In this paper, we demonstrate an efficient spectral approach to the simulation of multimode instabilities via a quantitative analysis of the instability of single-frequency lasing in ring lasers, referred to as the Lorenz-Haken (LH) instability or the Risken-Nummedal-Graham-Haken (RNGH) instability in distinct parameter regimes. Our approach, referred to as CFTD, uses generally non-Hermitian Constant Flux modes to obtain projected Time Domain equations. CFTD provides excellent agreement with finite-difference integration of the Maxwell-Bloch equations across a wide range of parameters in regimes of non-stationary inversion, including frequency comb formation and spatiotemporal chaos. We also develop a modal linear stability analysis using CFTD to efficiently predict multimode instabilities in lasers. The combination of numerical accuracy, speedup, and semi-analytic insight across a variety of dynamical regimes make the CFTD approach ideal to analyze multimode instabilities in lasers, especially in more complex geometries or coupled laser arrays.

physics.optics↗